To run an independent circuit, if you've a standard 2 story house, they'll take a new cable from your fuse board, and run it up into the ceiling. They'll lift floor boards in the room above, and take the cable across to partition wall between bedrooms, and route the cable up into the attic (you'll already have lots of cables following this route), then across attic to the back of house, outside, and down the back wall.
Run cable to shed, and terminate at an RCD, and wire your shed from there.
As suggested above, 4mm square cable will give you flexibility to do anything you want in future. The sockets in your house are on 2.5mm cable.
If you don't have a need for anything heavy duty in shed, what some people would do us run a spur from the kitchen socket circuit our to the shed. Much easier cause you just drill a hole in the wall, but you're limited to about the equivalent of an extension lead - so no welding!. I'm not an electrician obviously, so I don't know if this approach meets current standards.